In this paper, we design and validate a robust H∞ controller for Cooperative Adaptive Cruise Control (CACC) in connected vehicles. CACC systems take advantage of onboard sensors and wireless technologies working together in order to achieve smaller inter-vehicle following distances, with the overall goal of increasing vehicle throughput on busy highways, and hence serving as a viable approach to reduce traffic congestion. A group of connected vehicles equipped with CACC technology must also ensure what is known as string stability. This requirement effectively dictates that disturbances should be attenuated as they propagate along the platoon of following vehicles. In order to guarantee string stability and to cope with the uncertainties seen in the vehicle model used for a model-based CACC, we propose to design and implement a robust H∞ controller. Loop shaping design methodology is used in this paper to achieve desired tracking characteristics in the presence of competing string stability, robustness and performance requirements. We then employ model reduction techniques to reduce the order of the controller and finally implement the reduced-order controller on a simulation model demonstrating the robust properties of the closed-loop system.